If a baker sells loaves at 60p each, he sells 200 loaves per day. He finds that his sales are reduced by 5 loaves for each additional 1p he charges. If he sells at 67p, how many loaves will he sell?
160
165
193
195
An equation links the number of loaves (n) sold by a baker, in question 1, and the price (x pence) at which he sells them. This equation is:
n = 200 – 5x
n = 200 – 5(x – 60)
n = 195x - 60
n = 60x - 200
20 men working on the production line can produce 600 items per day with every extra man increasing the production by 50 items. If 26 men work on the line on one particular day, how many items will be produced?
900
770
730
650
An equation links the number of items (n) coming off the production line in question 3 with the number of men (m) working on the line. This equation is:
n = - 400 + 50m
n = 600 – 50m
n = 580 – 50m
n = 650 + 20m
The solution to the equation: 4x + 12 = 20 is:
x = 8
x = 5/4
x = 32
x = 2
The solution to the equation: 3x - 1 = 4 - 2x is:
x = 5
x = 3
x = 1
x = 1/2
The solution to the equation: 7x - 4 = 3 + 9x is:
x = 7/16
x = 3 1/2
x = -3 1/2
x = 1/2
The solution to the equation: 2(x - 3) = 3(1 - 2x) is:
x = 1 1/3
x = 1 1/8
x = 3/4
x = 4/9
The solution to the equation: 3x/4 = 12 is:
x = 2 2/3
x = 16
x = 9
x = 1
The solution to the equation: 3/ x - 1 = 1/2 is:
x = 1 1/6
x = 2 ½
x = 7
x = 1
When solving the quadratic equation ax2 + bx + c = 0 it is true that:
when b2 is bigger than 4ac, there are two real solutions to the equation
when b2 is equal to 4ac, there is no real solution to the equation
when b2 is smaller than 4ac, there is one real solution to the equation
none of the above is true.
The solution(s) to the equation equation: x2 + 2x + 1 = 0 is or are:
x = -1 or 1
x = -1 or 1
x = -1 or 0
x = -1
The solution(s) to the equation equation: 3x2 – 4x + 1 = 0 is or are:
x = 3 or 1
x = 1/3 or 1
x = 1/3 or -1
x = 3 or -1
The solution(s) to the equation equation: 4x2 – 3x = 0 is or are:
x = 0 or 3/4
x = 0 or 1 1/3
x = 3 or 4
x = 3/4 or 1 1/3
The solution(s) to the equation equation: 6 + x – x2 = 0 is or are:
x = 2 or -3
x = -3 or 2
x = 3 or -2
x = -3 or -2
The solution(s) to the equation equation: x2 = 1 – 2x = 0 is or are:
x = 1 – √2 or -1 + √2
x = 1 – √2 or 1 + √2
x = -1 – √2 or -1 + √2
x = -1 – √2 or 1 + √2
Remembering that profit (P) = revenue (R) – costs (C), and knowing that the number of items sold (n) = 600 – 5p (where £p is the selling price), the formula for the revenue (£R) in terms of p is:
R = £(600 – 5p)
R = £(600 – 5p2)
R = £(600p – 5p2)
R = £595p
If the cost (C) of producing n items is £200 + 3n, the equation needed to find the Profit in terms of the selling price is:
P = £(-2000 + 615p – 5p2)
P = £(2000 + 525p – 5p2)
P = £(2000 + 615p – 5p2)
P = £(-2000 + 525p – 5p2)
Solving this equation to find the selling price (p) when the profit is £0 gives p = :
£3.30 or £119.70
£3.0 or £120.00
£2.90 or £126.20
£13.00 or £110.00
Solving the simultaneous eqations: x + y = 3 and 3x – y = 5 gives the solution:
x = 2, y = 1
x = 2, y = -1
x = -2, y = 1
x = -2, y = -1
Solving the simultaneous eqations: 8x + 9y = 0 and 12x + 6y = 5 gives the solution:
x = 3/4, y = 2/3
x = 3/4, y = -2/3
x = 1 1/2, y = 2/3
x = 1 1/4, y = 0
Solving the simultaneous eqations: 5x + 2y = 3 and 4x + 2 = 5y gives the solution:
x = 1/3, y = 1/3
x = 2/3, y = 2/3
x = 1/3, y = 2/3
x = 2/3, y = 1/3
The time (T) taken in minutes to cook a joint of meat is given by forty times its weight (W) in kilograms plus another 30 minutes. The formula for this time and the time taken to cook a joint weighing 7 kilograms are:
T = 30W + 40, 4 hour 10 mins
T = 30W + 70, 4 hours 40 mins
T = 40W + 40, 5 hours 20 mins
T = 40W + 30, 5 hours 10 mins
An square office is to be constructed in a new building so that its floor area = F m2. Produce a formula to calculate the total area (W m2) of its walls if their height is H m.
W = 4H√F m2
W = 2√(HF) m2
W = 4HF m2
W = 4√(HF) m2
The formula for calculating degrees Fahrenheit from degrees Celcius is: F° = C° × 9/5 + 32°. Rearrange it so that C° becomed the subject of the formula.
C = 5/9 F+ 32
C = 5/9 F- 32
C = 5/9 (F+ 32)
C = 5/9 (F - 32)
The volume of a sphere in terms of its radius is v = 4/3 π r3. Make r the subject of the formula.
r = (3πv/4) 1/3
r = 3v1/3 /4π
r = (3v/ 4π) 1/3
r = 1/π (3v/4) 1/3
State the range of values of x for which 2x + 4 < 22
x < 7
x < 9
x < 13
x < 15
State the range of values of x for which 2 – ½ x > 5
x > 6
x < 1/5
x > 1/5
x < -6
State the range of values of x for which 13 > x + 2 > 10 – x
11 > x > 4
11 > x > 10
13 > x > 8
13 > x > -3
A production manager needs 0.5 man-hours to produce each item A and 1 man-hour to produce each item B. On a certain 8 hour day when he has 4 workers available he needs to produce at least a of item A and b of item B. The equation showing him this inequality in man-hours is: